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Seismic energy and stress-drop parameters for a composite source model

Seismological Laboratory and Department of Geological Sciences University of Nevada, Reno, Nevada 89557

Abstract

This article examines relationships among radiated energy and several stress-drop parameters that are used to describe earthquake faulting. This is done in the context of a composite source model that has been quite successful in its ability to reproduce statistical characteristics of strong-motion accelerograms. The main feature of the composite source model is a superposition of subevents with a fractal distribution of sizes, but all with the same subevent stress drop (_d) that is independent of the static stress drop (_s). In the model, _d is intended to represent the effective dynamic stress, and it does this well when _d > 2_s. The radiated energy in the S wave is E^CS_S = 0.233 C_E (_d/µ) M₀, where M₀ is the seismic moment of the earthquake, µ is shear modulus, and C_E is a dimensionless parameter that equals unity when _d > 2_s. The apparent stress (_a) is _a = 0.243 C_{E d}. The effective stress is _e 0.44C_{E d}. The Orowan stress drop (_o) is _o = 0.486 _d. The root-mean-square (rms) stress drop (_rms) is _rms = _dI^1/2M₀/M_os(R_max)^1/2 (f_c/f_o)^1/2, where f₀ is corner frequency of the earthquake, M_os (R_max) and f_c are the moment and corner frequency of the largest subevent, and I^1/2 is a dimensionless constant approximately equal to 1.7. Finally, the Savage-Wood ratio (SWR) is given by SWR C_{E d}/2 _s. These results clarify the relationships among all of these stress parameters in the context of a complex fault, showing the critical role of the subevent stress drop. They also provide an additional tool for energy, stress, and Savage-Wood ratio estimation. Since the process of modeling strong motion with the composite source uses realistic Green's functions, estimates of energy and stress parameters using this model are expected to have a good correction for wave propagation.

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